Answer:
a) 8.13
b) 4.10
Step-by-step explanation:
Given the rate of reaction R'(t) = 2/t+1 + 1/√t+1
In order to get the total reaction R(t) to the drugs at this times, we need to first integrate the given function to get R(t)
On integrating R'(t)
∫ (2/t+1 + 1/√t+1)dt
In integration, k∫f'(x)/f(x) dx = 1/k ln(fx)+C where k is any constant.
∫ (2/t+1 + 1/√t+1)dt
= ∫ (2/t+1)dt+ ∫ (1/√t+1)dt
= 2∫ 1/t+1 dt +∫1/+(t+1)^1/2 dt
= 2ln(t+1) + 2(t+1)^1/2 + C
= 2ln(t+1) + 2√(t+1) + C
a) For total reactions from t = 1 to t = 12
When t = 1
R(1) = 2ln2 + 2√2
≈ 4.21
When t = 12
R(12) = 2ln13 + 2√13
≈ 12.34
R(12) - R(1) ≈ 12.34-4.21
≈ 8.13
Total reactions to the drugs over the period from t = 1 to t= 12 is approx 8.13.
b) For total reactions from t = 12 to t = 24
When t = 12
R(12) = 2ln13 + 2√13
≈ 12.34
When t = 24
R(24) = 2ln25 + 2√25
≈ 16.44
R(12) - R(1) ≈ 16.44-12.34
≈ 4.10
Total reactions to the drugs over the period from t = 12 to t= 24 is approx 4.10
-5,-20,-80 find the common ratio
Answer:
The common ratio is 4
Step-by-step explanation:
To find the common ratio take the second term and divide by the first term
-20/-5 = 4
To verify take the third term and divide by the second
-80/-20 = 4
The common ratio is 4
Answer:
4
Step-by-step explanation:
To find the common ratio, divide one term by the term before it.
-20 ÷ -5 = 4
-80 ÷ -20 = 4
Each number is multiplied by 4 to get to the next number.
I hope this helps :))
Which solution set is graphed on the number line?
1
4
x>1
0 x > 1
Ox<1
X31
Answer:
4
Step-by-step explanation:
ur welcome hopefully this helps
Quick Start Company makes a 12-volt car batteries. After many years of product testing, the company knows the average life of a Quick Start battery is normally distributed, with mean=45 months and a std. deviation = 8 months.
If Quick start guarantees a full refund on any battery that fails within the 36 month period after purchase, what percentage of its batteries will the company expect to replace?
If quick Start does not want to make refunds for more than 10% ofits batteries under the full refund guarantee policy, for how longshould the company guarantee the batteries (to the nearest month)
Answer:
The company will expect to replace 13.03% of batteries.
The company should guarantee the batteries for 35 months.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 45, \sigma = 8[/tex]
If Quick start guarantees a full refund on any battery that fails within the 36 month period after purchase, what percentage of its batteries will the company expect to replace?
This is the pvalue of Z when X = 36. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{36 - 45}{8}[/tex]
[tex]Z = -1.125[/tex]
[tex]Z = -1.125[/tex] has a pvalue of 0.1303.
The company will expect to replace 13.03% of batteries.
If quick Start does not want to make refunds for more than 10% ofits batteries under the full refund guarantee policy, for how longshould the company guarantee the batteries
They should guarantee to the 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 45}{8}[/tex]
[tex]X - 45 = -1.28*8[/tex]
[tex]X = 34.76[/tex]
Rounding to the nearest month
The company should guarantee the batteries for 35 months.
what function is increasing? will give brainlist !
Answer:
Option B.
Step-by-step explanation:
Option A.
f(x) = [tex](0.5)^{x}[/tex]
Derivative of the given function,
f'(x) = [tex]\frac{d}{dx}(0.5)^x[/tex]
= [tex](0.5)^x[\text{ln}(0.5)][/tex]
= [tex]-(0.693)(0.5)^{x}[/tex]
Since derivative of the function is negative, the given function is decreasing.
Option B. f(x) = [tex]5^x[/tex]
f'(x) = [tex]\frac{d}{dx}(5)^x[/tex]
= [tex](5)^x[\text{ln}(5)][/tex]
= [tex]1.609(5)^x[/tex]
Since derivative is positive, given function is increasing.
Option C. f(x) = [tex](\frac{1}{5})^x[/tex]
f'(x) = [tex]\frac{d}{dx}(\frac{1}{5})^x[/tex]
= [tex]\frac{d}{dx}(5)^{(-x)}[/tex]
= [tex]-5^{-x}.\text{ln}(5)[/tex]
Since derivative is negative, given function is decreasing.
Option D. f(x) = [tex](\frac{1}{15})^x[/tex]
f'(x) = [tex]-15^{-x}[\text{ln}(15)][/tex]
= [tex]-2.708(15)^{-x}[/tex]
Since derivative is negative, given function is decreasing.
Option (B) is the answer.
Calculating the standard deviation (σ) for a list of n data values: 1. Calculate the average value. 2. Subtract the average value from each individual data value and enter the results in a column to the right of the data values. 3. Square each of the results obtained in step 2, and enter these in a new column to the right. 4. Sum the squares obtained in step 3. 5. Divide the result from step 4 by (n - 1) (the total number of measurements minus 1). 6. Take the square root of the result from step 5. This is the standard deviation. Expressed as an equation, the standard deviation of n measurements of data value x is: σ = ( Σ (x - xavg)2 / (n - 1) )1/2 Using the 6 steps above (or the spreadsheet function), calculate the standard deviation for the six values on page 16 and enter your answer below. Enter your result with only one sig fig, and remember to use a zero before the decimal point for values less than 1, for example 0.05 or 0.01.
Answer:
Step-by-step explanation:
The missing list of the data values for the question are as follows:
1 1.03
2 1.01
3 0.96
4 0.96
5 0.99
6 1
7 1.01
8 0.98
9 1.02
10 1.03
11 1
12 0.99
13 1
14 0.97
15 1.01
[tex]x_i[/tex] [tex](x_i - \bar x)[/tex] [tex](x_i - \bar x)^2[/tex]
1 1.03 0.03 0.0009
2 1.01 0.01 0.0001
3 0.96 -0.4 0.0016
4 0.96 -0.4 0.0016
5 0.99 -0.1 0.0001
6 1 0.0 0.0
7 1.01 0.1 0.0001
8 0.98 -0.2 0.0004
9 1.02 0.2 0.0004
10 1.03 0.3 0.0009
11 1 0.0 0.0
12 0.99 -0.1 0.0001
13 1 0.0 0.0
14 0.97 -0.03 0.0009
15 1.01 0.1 0.0001
The average value for x is calculated as:
[tex]\bar x = \dfrac{14.96}{15}[/tex]
[tex]\bar x = 0.997 \\ \\ \bar x \approx 1.00[/tex]
[tex]\sum (x-x_i)^2 = 0.0072[/tex]
[tex]\dfrac{\sum (x-x_i)^2 }{n-1}= \dfrac{0.0072}{15-1} \\ \\ = \dfrac{0.0072}{14} \\ \\ = 0.00051[/tex]
[tex]\sigma = \sqrt{\dfrac{\sum (x-x_i)^2 }{n-1}} = \sqrt{0.00051} \\ \\ \sigma =0.0226 \\ \mathbf { \\ \sigma =0.02 \ to \ one \ significant \ figure}[/tex]
How do I find the value of x for which line a is parallel to line b?
Answer:
x = 20
Step-by-step explanation:
3x + 6x = 180, if you make them supplementary then they will be parallel
9x = 180
x = 20
Two competing gyms each offer childcare while parents work out Gym A charges $9.00 per hour of childcare. Gym B
charges $0.75 per 5 minutes of childcare. Which comparison of the childcare costs is accurate?
Answer:
They charge an equal amount of money each hour.
Answer:
Gym B and Gym A charge the same hourly rate for childcare.
Step-by-step explanation:
answer on edge
I need help please help
Answer:
Step-by-step explanation:
Note that 28 + 110 + 42 = 180, and that 28 + 42 + 110 = 180 also.
Since all three angles of one triangle are the same as the corresponding angles of the other triangle, the triangles are similar.
The average number of children a Japanese woman has in her lifetime is 1.37. Suppose that one Japanese woman is randomly chosen. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X.X~ _____(_____,_____) d. Find the probability that she has no children. e. Find the probability that she has fewer children than the Japanese average.
Answer:
a. X: amount of children that a Japanese woman has in her lifetime.
b. X can take natural numbers (all positive integers) as values.
c. X~Poi(1.37).
d. P(X=0)=0.2541
e. P(X<1.37)=0.6022
Step-by-step explanation:
a) This can be modeled with a Poisson distribution.
We let the variable X be the amount of children that a Japanese woman has in her lifetime.
The parameter of the Poisson distribution is λ=1.37.
This is also the value of the mean and the standard deviation.
b) X can take all positive integer values.
c) X is modeled as a Poisson variable with λ=1.37.
d) This can be calculated as:
[tex]P(0)=\lambda^ke^{-\lambda}/k!=1.37^{0} \cdot e^{-1.37}/0!=1*0.2541/1=0.2541\\\\[/tex]
e) Having fewer children than the average means that she has one or none children.
This can be calculated as:
[tex]P(X<1.37)=P(0)+P(1)\\\\\\P(0)=1.37^{0} \cdot e^{-1.37}/0!=1*0.2541/1=0.2541\\\\P(1)=1.37^{1} \cdot e^{-1.37}/1!=1.37*0.2541/1=0.3481\\\\\\P(X<1.37)=0.2541+0.3481=0.6022[/tex]
simplify 2^3 ÷ 2^-3
leave your answer in the form 2^x, where x is an integer
these are the options for the answer
1
0
2^0
2^6
Answer:
[tex]2^{6}[/tex]
Step-by-step explanation:
[tex]2^3 \div 2^{-3}[/tex]
[tex]2^{3-(-3)}[/tex]
[tex]2^{3+3}[/tex]
[tex]2^{6}[/tex]
Select the correct answer
Why are online payment services necessary?
OA
Individuals who sell items online cannot afford to deal with credit card companies.
B.
It is too risky to use credit cards online, and online payment services have better security
C. Government regulations require all online transactions be made using online payment services.
D.
Online payment services are the only payment method that individuals who sell items online trust.
Reset
Nalut
Answer:
B
Step-by-step explanation:it is really too risky to use credit card online because for someone who doesnt now if the busines is really considered as a trustful source or just a scam.
Answer:
Its A.) Individuals who sell items online cannot afford to deal with credit card companies.
Step-by-step explanation:
On plato
Using the data in the table, use the exponential smoothing method with alpha=0.5 and a February forecast of 500 to forecast
sales for May
Month Demand
January 480
February 520
March 535
April 550
May 590
June 630
Answer:
Step-by-step explanation:
The formula to calculate the forecast could be determine by using the exponential smoothing method :
[tex]Ft = F(t-1) + \alpha [A(t-1) - F(t-1)][/tex]
Where ,Ft is the Forecast for period t
F(t-1) is the Forecast for the period previous to t
A(t-1) is the Actual demand for the period previous to t
[tex]\alpha[/tex] = Smoothing constant
To get the forecast for may and june the above formula with [tex]\alpha =0.5[/tex] and april forecast of 500 will be used
For march
[tex]=500+0.5(520-500)\\\\=500+0.5\times20\\\\=500+10\\\\=510[/tex]
For April
[tex]=510+0.5(535-510)\\\\=510+0.5\times25\\\\=510+12.5\\\\=522.5[/tex]
For May
[tex]=522.5+0.5(550-5225)\\\\=522.5+0.5\times27.5\\\\=522.5+13.75\\\\=536.25[/tex]
So forecast for May = 536.25
Assume that the heights of men are normally distributed with a mean of 70.9 inches and a standard deviation of 2.1 inches. If 36 men are randomly selected, find the probability that they have a mean height greater than 71.9 inches. Round to four decimal places.
Answer:
The probability that they have a mean height greater than 71.9 inches
P( x⁻ ≥71.9) = 0.0022
Step-by-step explanation:
Explanation:-
Given mean of the Population μ= 70.9
Standard deviation of the Populationσ = 2.1
Given sample size 'n' =36
let x⁻ be the mean height
given x⁻ =71.9 inches
[tex]Z=\frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z=\frac{71.9 -70.9}{\frac{2.1}{\sqrt{36} } } = \frac{1}{0.35} = 2.85[/tex]
The probability that they have a mean height greater than 71.9 inches
P( x⁻ ≥71.9) = P(Z ≥ 2.85)
= 1 - P(Z≤ 2.85)
= 1 - ( 0.5 + A(2.85)
= 0.5 - A( 2.85)
= 0.5 - 0.4978
= 0.0022
The probability that they have a mean height greater than 71.9 inches
P( x⁻ ≥71.9) = 0.0022
Answer:
the answer is 0.0022
Step-by-step explanation:
The value z is directly proportional to c. When z = 20, c = 10. Find an equation relating z and c. *
Answer:
a) The equation of Z and C is Z =K C
b) K = 2
Step-by-step explanation:
Explanation :-
Given data Z is directly proportional to C
⇒ Z ∝ C
⇒ Z = K C
The equation of relating Z and C
Z = K C
Given Z = 20 and C =10
20 = K ( 10)
⇒ K = 2
Factorizar e indicar cuántos factores primos tiene -3+3x^2+y-x^2*y-y^2+x^2*y
What is another way to write 2×5 without using the multiplication sign?
Answer:
see below
Step-by-step explanation:
You could write it as 2+2+2+2+2 or 5+5 bc multiplication is like repeated addition.
Answer:
You can use the repeated additional as given below.
Step-by-step explanation:
2+2+2+2+2 or 5+5
Brian invests £6300 into his bank account.
He receives 4.9% per year compound interest.
How much will Brian have after 2 years?
Give your answer to the nearest penny where appropriate.
Answer:
Amount that Brian has after 2 years = £6932.53
Step-by-step explanation:
To find, the amount that Brian will have after 2 years:
Formula for amount where compound interest is applicable:
[tex]A = P \times (1+\dfrac{R}{100})^t[/tex]
Where A is the amount after t years time
P is the principal.
R is the rate of interest.
In the question, we are given the following details:
Principal amount,P = £6300
Rate of interest,R = 4.9%
Time,t = 2 years
Putting the values in formula:
[tex]A = 6300 \times (1+\dfrac{4.9}{100})^2\\\Rightarrow 6300 \times (\dfrac{104.9}{100})^2\\\Rightarrow 6932.53[/tex]
Hence, Amount that Brian has after 2 years = £6932.53
Answer:
THE ANSWER IS ABOVE
Step-by-step explanation:
hahahaha
Write an expression without exponent that is equivalent to 2 to 3rd power nd 4 to the 3rd power
Answer:
8 and 64
Step-by-step explanation:
[tex]2^3[/tex] and [tex]4^3[/tex]
[tex]2^3=8[/tex]
[tex]4^3=64[/tex]
The probability that a can of paint contains contamination is 3.23%, and the probability of a mixing error is 2.4%. The probability of both is 1.03%. What is the probability that a randomly selected can has contamination or a mixing error?
Answer:
4.6%.
Step-by-step explanation:
The probability that a can of paint contains contamination(C) is 3.23%
P(C)=3.23%
The probability of a mixing(M) error is 2.4%.
P(M)=2.4%
The probability of both is 1.03%.
[tex]P(C \cap M)=1.03\%[/tex]
We want to determine the probability that a randomly selected can has contamination or a mixing error. i.e. [tex]P(C \cup M)[/tex]
In probability theory:
[tex]P(C \cup M) = P(C)+P(M)-P(C \cap M)\\P(C \cup M)=3.23+2.4-1.03\\P(C \cup M)=4.6\%[/tex]
The probability that a randomly selected can has contamination or a mixing error is 4.6%.
Which number best represents the location of the point on the line?
X
-4.44
-T
11
3
_V17
RETRY
Answer:
- 11 over 3 Just did it on edg 2021
Find the VOLUME of this composite solid.
Answer:
(294π +448) cm³ ≈ 1371.6 cm³
Step-by-step explanation:
The half-cylinder at the right end has a radius of 7 cm, as does the one on top. Together, the total length of these half-cylinders is 8 cm + 4cm = 12 cm. That is equivalent in volume to a whole cylinder of radius 7 cm that is 6 cm long.
The cylinder volume is ...
V = πr²h = π(7 cm)²(6 cm) = 294π cm³
__
The cuboid underlying the top half-cylinder has dimensions 4 cm by 8 cm by 14 cm (twice the radius). So, its volume is ...
V = LWH = (4 cm)(8 cm)(14 cm) = 448 cm³
Then the total volume of the composite figure is ...
(294π +448) cm³ ≈ 1371.6 cm³
Want to donate to a better cause? Consider micro-lending. Micro-lending is a process where you lend directly to entrepreneurs in developing countries. You can start lending at $25. Kiva.org boasts a 99% repayment rate. The average loan to an entrepreneurs is $388.44 and the average loan amount is $261.14. With a total amount loaned of $283,697,150, how many people are lending money if the average number of loans per lender is 8?
Answer:
135,797
Step-by-step explanation:
If the total loan amount is $283,697,150 and the average loan amount is $261.14, then the number of loans is ...
$283,697,150/$261.14 = 1,086,379.5
If the average number of loans per lender is 8, then the number of lenders is ...
1086379.5/8 = 135,797 . . . . people lending money
Example and answer,will give brain
Answer:
b) -2/5
Step-by-step explanation:
b is -2/5 because its negative and goes down at a rate of 0.4 or 2/5
a , ummmm IDK that, sorry
Brainliest, crown to me
What is the mixed number3 3/8 as a fraction
Answer: Mixed Number to Fraction
Mixed Numbers to Improper Fraction
Mixed Numbers Improper Fraction
3 3/4 15/4
3 3/8 27/8
3 8/9 35/9
Hope this helps!!
A 15-inch candle is lit and steadily burns until it is burned out. Let b represent the burned length of the candle (in inches) and let r represent the remaining length of the candle (in inches).
a. Write a formula that expresses r in terms of b.When 3.1 inches have burned from the candle, the remaining length of the candle is inches.
b. Graph the relationship between a and b
Answer:
(a)r=15-b
11.9 Inches
(b)See attached
Step-by-step explanation:
Length of the candle =15 inch
Let b represent the burned length of the candle (in inches)
Let r represent the remaining length of the candle (in inches).
Therefore:
(a) r+b=15
r=15-b
When b=3,1 Inches
Remaining Length, r=15-3.1=11.9 Inches
(b)The graph showing te relationship between r and b is shown below.
r is plotted on the y-axis while b is plotted on the x-axis as labelled.
Formula that express r in terms of b is
[tex]r=15-b[/tex]
Remaining length of candle is 11.9 inches
Given :
A 15-inch candle is lit and steadily burns until it is burned out
Let b represent the burned length and let r represent the remaining length
We need to write the formula
remaining length = initial length - burned length
[tex]r=15-b[/tex]
When 3.1 inches have burned from the candle, the remaining length of the candle is inches.
b is 3.1
remaining length [tex]r=15-3.1=11.9[/tex] inches
now we graph the relationship
Graph is attached below.
Learn more : brainly.com/question/13844802
An amount was invested at % r per quarter. What value of rwill ensure that accumulated amount at the end of one year is 1.5 times more than amount invested? Correct to 2 decimal places
Answer:
42.67%
Step-by-step explanation:
The annual growth factor for interest at annual rate r compounded quarterly is ...
(1 +r/4)^4
You want that value to be 1.5:
1.5 = (1 +r/4)^4
1.5^(1/4) = 1 +r/4
(1.5^(1/4) -1) = r/4
4(1.5^(1/4) -1) = r ≈ 0.426728
The rate r must be about 42.67%.
_____
Comment on the wording
We interpreted the problem to mean the end-of-year amount is 1.5 times the beginning-of-year amount. That is, it is "1.5 times the amount invested."
The word "more" is typically used when addition is involved. For example, "25% more" means 25% of the original is added to the original. We occasionally see "more" where "x times more" is intended to mean "x times", rather than "x times the amount, added to the original amount."
Solve the equation. 3= x/3.3 what is x=
Answer:
9.9
Step-by-step explanation:
remember your distribution rules.
x/3.3=3 make sure x is by itself. so take 3*3.3
When you have x divided by a number equaling a number take the number it equals to and multiply by the number that x is being divided by.
3=x/3.3
move 3.3 by multiplying it by 3 which gives you 9.9.
The solution of x in equation 3 = x / 3.3 is,
⇒ x = 9.9
We have to given that;
Expression is,
⇒3 = x / 3.3
Now, We can simplify the equation for x as;
⇒ 3 = x / 3.3
Multiply by 3.3 both side,
⇒ 3 × 3.3 = x
⇒ 9.9 = x
⇒ x = 9.9
Thus, Solution is,
⇒ x = 9.9
Learn more about the equation visit:
brainly.com/question/28871326
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Mary is three quarters of Cameron's age. Mary is 24 years old. How old is Cameron?
Answer:
32 years oldStep-by-step explanation:
3/4=24 so 1/4= 24÷3= 8
1/4=8
So to get 4/4 or Cameron's age it is 8×4=32yrs
[tex]answer \\ 32 \: years \: old \\ solution \\ mary's \: age = 24 \\ let \: cameron's \: age \: be \: x \\ given \\ \frac{3}{4} x = 24 \\ or \: x = 24 \times \frac{4}{3} \\ x = 32 \\ hope \: it \: helps[/tex]
Seventy-six percent of sunflower seeds will germinate into a flower, and a sample of 800 such sunflower seeds is randomly selected. The standard deviation for the number of sunflower seeds that will germinate in such samples of size 800 is:
Answer:
12.08
Step-by-step explanation:
For each sunflower, there are only two possible outcomes. Either it germinates, or it does not. The probability of a sunflower germinating is independent of other sunflowers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Seventy-six percent of sunflower seeds will germinate into a flower
This means that [tex]p = 0.76[/tex]
Samples of 800:
This means that [tex]n = 800[/tex]
The standard deviation for the number of sunflower seeds that will germinate in such samples of size 800 is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.76*0.24} = 12.08[/tex]
It took jack 4 and half minutes to do 100 multiplication facts how long it takes him to do 150
Answer:
6.75 min
Step-by-step explanation:
100 facts/4.5 min = 150 facts/x min
x=(150*4.5)/100=6.75